Would-be Iraqi female suicide bomber Ms Sajida al-Rishawi and Iraqi Al-Qaeda member Mr Ziad al-Karboli were executed at 4:00 am local time (0200 GMT), Momani told AFP.
A security source said the executions were carried out at Swaqa prison south of the capital Amman.
Jordan had promised to begin executing death-row Islamic extremists at daybreak in response to the murder of Mr Maaz al-Kassasbeh, who was captured by IS when his plane went down in December.
Ms Rishawi, 44, was condemned to death for her participation in deadly attacks in Amman in 2005 and IS had offered to spare Mr Kassasbeh's life and free a Japanese hostage, who was later beheaded, if she were released.
Jordan had on February 3 vowed an "earth-shattering" response to the killing of Kassasbeh, hours after a harrowing video emerged online purporting to show the captive and caged 26-year-old F-16 fighter pilot engulfed in flames.
© 1994-2015 Agence France-Presse